When he arrived in San Francisco to compete in the 1955 U.S. Open, Jack Fleck was giving golf one last try. He was 33 years old and had never finished higher than eighth in a sanctioned tournament.

Few golfers were more obscure. Mr. Fleck worked at two municipal courses in his native Iowa and barely qualified for the U.S. Open, the country’s most prestigious golf tournament. He had little going for him but hope, faith and a new set of golf clubs designed by Ben Hogan, generally acknowledged to be the best golfer in the world.

By the end of the week, Mr. Fleck and Hogan would walk side by side into history in what is still regarded as one of golf’s most memorable moments.

Mr. Fleck was 92 when he died March 21 in Fort Smith, Ark. He was 92. His wife, Carmen Fleck, confirmed his death but did not disclose a cause.

A self-taught golfer, Mr. Fleck had an easy, natural swing but tended to struggle on the greens with his putting.

While practicing during the week before the U.S. Open — then usually called the National Open — Mr. Fleck took careful note of the undulating par-70 course at the Olympic Club. The night before the tournament began, Hogan presented Mr. Fleck with two newly made clubs to complete his set.

In the first round, Mr. Fleck shot a mediocre 76, followed by a sparkling 69 the next day. The final two rounds — 36 holes in all — were played on Saturday, June 18.

Mr. Fleck was 6-feet-1 and weighed 164 pounds and was one of the first American athletes in any sport to make yoga part of his workouts, saying it gave him greater self-composure. He did not drink, smoke or eat red meat.

He was openly religious throughout his life, but he refused to pray for victory — only for “the power and strength to compete,” according to “The Longest Shot,” a 2012 book by Neil Sagebeil.

The morning of the final two rounds, Mr. Fleck had an experience in his hotel room that had never happened to him before — and that he would not speak of for decades.

“I was shaving, and suddenly a voice came out of the glass, clear as a bell,” he told author James Dodson for the 2004 biography “Ben Hogan: An American Life.” “It said, ‘Jack, you are going to win the Open.’ At first I thought I’d imagined it or maybe somebody was in the room with me. I looked around, then went back to shaving. By golly, if it didn’t come a second time — straight out of the mirror. Clear as day. ‘Jack, you are going to win the Open!’ I had goose bumps on me, as if electricity was going through my body.”

Mr. Fleck didn’t say a word to anyone as he went out to the golf course. He shot a 75 in the third round, leaving him tied for sixth place, three strokes behind Hogan.

In the final round, Hogan shot a 70 and seemed to have an insurmountable lead. He was congratulated on what would have been a record fifth U.S. Open title.

But Mr. Fleck was still on the course, playing inspired golf. He scored a birdie on the 15th hole and, after pars on 16 and 17, needed a birdie on the par-4 18th hole to finish in a tie. On his second shot, Mr. Fleck used the Hogan-designed 7-iron to loft the ball firmly onto the green, seven feet from the cup. He calmly sank the tricky downhill putt to finish at 67, tying Hogan’s four-round total of 287.

The next day, the two players met for an 18-hole playoff. The 42-year-old Hogan, limping from injuries he sustained in a near-fatal auto accident in 1949, “was controlling the ball, hitting the fairways, hitting the greens, retaining his composure,” golf writer Herbert Warren Wind wrote in Sports Illustrated.

Hogan sank a 50-foot putt at No. 8, but Mr. Fleck dropped in a 25-foot putt for a birdie on the ninth hole. With Mr. Fleck leading by three shots, Hogan fought back with birdies on 14 and 17. By the time they reached the final hole, Mr. Fleck led by a single stroke.

At No. 18, Hogan’s foot slipped slightly on his drive, causing the ball to hook left of the fairway. He needed three shots to escape the tall grass of the rough and ended up scoring a double-bogey 6.

Mr. Fleck finished with a par 4 on 18 to win the playoff by three strokes, 69 to 72.

The upset resounded throughout the golf world and beyond. President Dwight D. Eisenhower asked to meet Mr. Fleck, and he was interviewed on television and asked to endorse products.

Mr. Fleck won two tournaments later in his career and finished tied for third at the 1960 U.S. Open, but he never had another moment like his duel with Hogan.

“Many historians,” Dodson wrote in his Hogan biography, “list Fleck’s Open play-off win as one of the biggest upsets in all of sports history.”

Jack Donald Fleck was born Nov. 8, 1921, in Bettendorf, Iowa, and grew up in poverty.

“My mother and father had the toughest life in the world,” he said in 2012. “There was just no money. We grew all the food that we ate, and my mother canned everything so we could eat in the winter.”

Mr. Fleck worked as a caddie in high school, competing in tournaments with borrowed clubs. He served in the Navy during World War II aboard a British ship that took part in the Normandy invasion.

In later years, he competed on the senior tour while teaching at rural golf courses in Arkansas. He continued to make appearances at major golf tournaments throughout his life, as the magic of the 1955 Open never seemed to fade.

His first wife, Lynn Burnsdale Fleck, died in 1975. His second wife, Mariann Fleck, died in 2000. Survivors include his wife of 13 years, Carmen Hall Fleck of Fort Smith; a son from his first marriage, Craig Fleck of Oroville, Calif.; a sister; a granddaughter; and a great-granddaughter.

In a memoir published late in his life, Mr. Fleck recalled the final hole of the 1955 U.S. Open, as evening shadows began to reach across the tree-lined fairway of the Olympic Club.

“The clouds let a few streaks of sunlight shine through,” he wrote. “And I said to myself, ‘If this isn’t heaven, I don’t know what is.’ ”